A298667 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 5, 2, 5, 1, 1, 1, 8, 8, 2, 2, 8, 8, 1, 1, 5, 7, 9, 20, 9, 7, 5, 1, 1, 22, 25, 13, 38, 38, 13, 25, 22, 1, 1, 29, 25, 26, 84, 169, 84, 26, 25, 29, 1, 1, 60, 58, 74, 319, 238, 238, 319, 74, 58, 60, 1, 1, 121, 95, 134, 770, 1019, 978

Offset

1,13

Comments

Table starts

.1..1..1..1...1....1.....1.....1......1.......1.......1........1.........1

.1..1..0..1...2....1.....8.....5.....22......29......60......121.......194

.1..0..3..1...5....8.....7....25.....25......58......95......155.......299

.1..1..1..2...2....9....13....26.....74.....134.....325......731......1568

.1..2..5..2..20...38....84...319....770....2106....6301....17282.....47774

.1..1..8..9..38..169...238..1019...3112....7518...25887....74736....218787

.1..8..7.13..84..238...978..3895..11843...49752..184380...640323...2550161

.1..5.25.26.319.1019..3895.22938..81474..386923.1791871..7595552..35648606

.1.22.25.74.770.3112.11843.81474.329249.1693779.9364144.43238329.235861179

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) for n>5

k=3: [order 12]

k=4: [order 35]

Example

Some solutions for n=8 k=4
..0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0
..1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
..0..1..1..1. .0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..1
..1..1..1..0. .1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..0..1
..1..1..1..1. .1..1..1..1. .1..0..1..1. .1..1..0..1. .1..1..1..1
..0..1..1..0. .0..1..1..0. .1..1..1..0. .0..1..1..1. .0..1..1..0
..1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
..0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0

Crossrefs

Column 2 is A297809(n-2).

Sequence in context: A253238 A249773 A030369 * A226166 A209155 A082062

Adjacent sequences: A298664 A298665 A298666 * A298668 A298669 A298670

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 24 2018

Status

approved